I have a large scene with a hierarchy of nested Empties. I need to select and delete all the objects under Empties with a specific name
This should be rather easy, if I didn't miss anything.

Select and delete all
Filter name through the search bar.
Press Enter to confirm the search.
Select all, shortcut A
RMB > Delete



Delete hierarchy
Deleting the whole hierarchy of empties for some reason doesn't work well in the outliner.
Just move your mouse over to the 3D viewport and it works well.
RMB > Select Hierarchy
Delete Key in the 3D viewport to delete selected.



The grayed out items are hidden objects.
To make them visible in your scene, use the outliner toggles: